Feasibility of sorting a basket of clothes in the real world
Peter Abbeel does work in deep learning for robotics, and one of the projects they've tackled is manipulating clothes. Here's a video from 2011 of their robot folding laundry (one piece at a time).

There are also companies attempting to market this; seven dreamers makes the Laundroid and Foldimate claims that it will start taking pre-orders in 2017.